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For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information transmission above which a given compact subset of the state…
This paper presents a new numerical abstract domain for static analysis by abstract interpretation. This domain allows us to represent invariants of the form (x-y<=c) and (+/-x<=c), where x and y are variables values and c is an integer or…
Shannon's sampling theorem is one of the cornerstone topics that is well understood and explored, both mathematically and algorithmically. That said, practical realization of this theorem still suffers from a severe bottleneck due to the…
Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…
The increasing computational requirements of deep neural networks (DNNs) have led to significant interest in obtaining DNN models that are sparse, yet accurate. Recent work has investigated the even harder case of sparse training, where the…
Shannon entropy is the shortest average codeword length a lossless compressor can achieve by encoding i.i.d. symbols. However, there are cases in which the objective is to minimize the \textit{exponential} average codeword length, i.e. when…
Approximate Bayesian computation (ABC) is a widely used inference method in Bayesian statistics to bypass the point-wise computation of the likelihood. In this paper we develop theoretical bounds for the distance between the statistics used…
We consider closed meandric systems, and their equivalent description in terms of the Hasse diagrams of the lattices of non-crossing partitions $NC(n)$. In this equivalent description, the number of components of a random meandric system of…
This paper presents a saddlepoint approximation of the random-coding union bound of Polyanskiy et al. for i.i.d. random coding over discrete memoryless channels. The approximation is single-letter, and can thus be computed efficiently.…
Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…
Finding optimal wave sampling methods has far-reaching implications in wave physics, such as seismology, acoustics, and telecommunications. A key challenge is surpassing the Whittaker-Nyquist-Shannon (WNS) aliasing limit, establishing a…
Generative Adversarial Networks (GANs) are powerful models able to synthesize data samples closely resembling the distribution of real data, yet the diversity of those generated samples is limited due to the so-called mode collapse…
We consider sparse superposition codes (SPARCs) over complex AWGN channels. Such codes can be efficiently decoded by an approximate message passing (AMP) decoder, whose performance can be predicted via so-called state evolution in the…
We provide a novel framework to study subspace codes for non-coherent communications in wireless networks. To this end, an analog operator channel is defined with inputs and outputs being subspaces of $\mathbb{C}^n$. Then a certain distance…
Neural networks have proven practical for a synergistic combination of advanced control techniques. This work analyzes the implementation of rectified linear unit neural networks to achieve constrained control in differentially flat…
Artificial Neural Networks (ANN) comprise important symmetry properties, which can influence the performance of Monte Carlo methods in Neuroevolution. The problem of the symmetries is also known as the competing conventions problem or…
As time series data become increasingly prevalent in domains such as manufacturing, IT, and infrastructure monitoring, anomaly detection must adapt to nonstationary environments where statistical properties shift over time. Traditional…
This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Numerous renowned algorithms for tackling the compressed sensing problem…
Our objective is to estimate the unknown compositional input from its output response through an unknown system after estimating the inverse of the original system with a training set. The proposed methods using artificial neural networks…
We study quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization of Strassen's theorem on preordered semirings. We find that an asymptotic variant of relative submajorization, defined on…